Robotic Finger Actuated with Shape Memory Alloy Tendon

Transcription

1 Robotic Finger Actuate with Shape Memory Alloy enon NICU-GEORGE BIZDOACA, ILIE DIACONU, MARIUS C. NICULESCU, ELVIRA BIZDOACA, SONIA DEGERAU, DANIELA PANA, CRISINA PANA Department of Automatics University of Craiova 5 ehnicii Street, Craiova, 00 ROMANIA Abstract: - In the present article is explore the kinematics an statics of shape memory alloy tenon-riven finger. Shape memory alloy offer other interesting solution, using the shape transformation of the wire/structure in the moment of applying a thermal type transformation able to offer the martensitic temperature. An extension function is use in orer to moel the routing of each tenon. he kinematics of the tenon network, combine with the ynamics of the mechanism is applie to a two-link tenon-riven finger using shape memory actuation. Numerical simulations are presente an observations are formulate. Key-Wors: - robotic finger, shape memory alloy, mathematical moeling, numerical simulation. Shape memory alloy materials he shape memory effect was first note over 50 years ago; it was not until 96, however, with the iscovery of a nickel titanium shape memory alloy but Buehler, that serious investigations were unertaken to unerstan the mechanism of the shape memory effect. he shape memory alloys possess the ability to unergo shape change at low temperature an retain this eformation until they are heate, at which point they return to their original shape. he nickel titanium alloys, use in the present research, generally referee to as Nitinol, have compositions of approximately 50 atomic % Ni/ 50 atomic % i, with small aitions of copper, iron, cobalt or chromium. he alloys are four times the cost of Cu-Zn-Al alloys, but it possesses several avantages as greater uctility, more recoverable motion, excellent corrosion resistance, stable transformation temperatures, high biocompatibility an the ability to be electrically heate for shape recovery. Shape memory actuators are consiere to be low power actuators an such as compete with solenois, bimetals an to some egree was motors. It is estimate that shape memory springs can provie over 00 times the work output of thermal bimetals. he use of shape memory alloy can sometimes simplify a mechanism or evice, reucing the overall number of parts, increasing reliability an therefore reucing associate quality costs. Because of its high rezistivity of micro ohm-cm, nickel titanium can be self heate by passing an electrical current through it. he basic rule for electrical actuation is that the temperature of complete transformation to martensite Mf, of the actuator, must be well above the maximum ambient temperature expecte. he alloys an manufacturing techniques improve, so i the experience an results of experimenters. Nitinol receive much attention for meical applications, toys inustry, teleoperate systems an robotics, especially autonomous robots. In 989 Oaktree Automation Inc, in Alexanria Virginia, starte eveloping the Finger spelling Han, an anthropomorphic robotic evice to serve as a tactile communication ai for eaf - blin iniviuals, particularly those unable to rea Braille. he evice use a total of one hunre an eight 50 µm Flexinol wires acting in parallel. he most successful applications of shape memory alloy components usually have all or most of the following characteristics: A mechanically simple esign he shape memory component pops in place an is hel by other parts in the assembly he shape memory alloy component is in irect contact with a heating/cooling meium Friction is minimize an no complex stresses or stress concentrations are present A minimum force an motion requirement for the shape memory component he shape memory component is isolate from inciental forces with high variation he tolerances of all the components realistically interface with the shape memory component. Base on escription of shape memory alloy

2 materials, a SMA Simulink block was evelope. he characteristic of material is iealize, but the approximations mae are suitable for an efficient simulation. he user can inicate the start an stop martensitic an austenitic temperature an the force, momentum evolution. Figure. Shape memory alloy block he numerical results respect the real comportment of the user specifie shape memory alloy: Figure. he SMA moel Figure. he response of the SMA moel to sinusoial energizing signal he electrical activation of SMA actuator imposes the following relations for the current, temperature an response time: For heating I I I I = 4,98 +,6 = K K + F F L L ( - maximum temperature, wire iameter, I electrical current, F L - require force t Heating meium = J h ln ( t Heating heating time, J h heating coefficient, meium meium temperature, A ambient temperature, - aim temperature upon heating J h = 6,7 +,9 = K J + K J F L ( For cooling H A 8,88 tc = J c ln + c A M S A (4 J c = 4,88 + 6,6 = K J + K J F c c L (5 t c cooling time, H - initial temperature upon cooling, A - ambient temperature, wire iameter, C - aim cooling temperature, J C - time constant for cooling, M S - martensitic start temperature. One can observe the time epenence of require force an require stroke. he electrical calculations for irect current heating etermine: he amount of current neee for actuation in the require time he resistance of the nickel titanium actuation element he voltage require to rive the current through element he power issipate by the actuation element. he first requirement can be establish using the material escription tables [9]. he resistance is etermine using the following expression:,09x0 Resistance / mm = Ω / mm (6 he voltage an power requirements results from: V = IR ; Power = I R (7 I current in amps, V voltage in volts, R resistance in Ω. In case of using pulse with moulation heating the following relation can be use: t uty cycle( % = x00 t (8 t the with of constant current pulse, t the total cycle time. 00 Pavr uty cycle( % = I i R (9 00 uty cycle( % = Pavr R Vi (0 P avg average pulse power (effective DC power, Ii applie pulse current, V i applie pulse voltage, R electric resistance.

3 Dynamics of two-link tenonriven finger here are many methos for generating the ynamic equations of mechanical system. All methos generate equivalent sets of equations, but ifferent forms of the equations may be better suite for computation ifferent forms of the equations may be better suite for computation or analysis. he Lagrange analysis will be use for the present analysis, a metho which relies on the energy proprieties of mechanical system to compute the equations of motion. We consier that each link is a homogeneous rectangular bar with mass mi an moment of inertia tensor I xi 0 0 I i = 0 I yi 0 ( 0 0 I zi Letting v i R be the translational velocity of the centre of mass for the i th link an ω i R be angular velocity, the kinetic energy of the manipulator is: ( θ, & θ = m v + mω Iω + m v + mω Iω ( Since the motion of the manipulator is restricte to xy plane, v i is the magnitue of xy velocity of the centre of mass an ω i is a vector in the irection of the y axis, with ω = & θ an ω = & θ & + θ.we solve for kinetic energy in terms of the generalize coorinates by using the kinematics of the mechanism. Let p i = ( xi, yi,0 enote the position of the i th centre of mass. Letting r an r be the istance from the joints to the centre of mass for each link, results x = r cos( θ ( x& = r & θ sin( θ (4 y = r sin( θ (5 y & = r & θ cos( θ (6 x = l cos( θ + r cos( θ + θ (7 x& = ( l sin( θ + r sin( θ + θ & θ r & θ sin( θ + θ (8 y = l sin( θ + r sin( θ + θ (9 y & = ( l cos( θ + r cos( θ + θ & θ r & θ cos( θ + θ (0 Using the kinetic energy an Lagranage methos results: α + βc δ + βc && θ + && δ + βc θ δ β s & θ β s (& θ + & θ & θ τ = ( & β s & θ 0 θ τ where m m α = ( l + w + ( l + w + mr + m ( l + r β = mll ( m δ = ( l + w + mr ; with w, w, l,l the with an respectively the length of link an link. Figure 4. wo link finger architecture ENDON ACUAED FINGERS Consier a finger which is actuate by a set of tenons such as the one shown in Figure 5. Each tenon consists of a cable connecte to a force generator. For simplicity we assume that each tenon pair is connecte between the base of the han an a link of the finger. Interconnections between tenons are not allowe. he routing of each tenon is moelle by an extension function h i : Q R. he extension function measures the isplacement of the en of the tenon as a function of the joint angles of the finger. he tenon extension is a linear function of the joint angles hi ( θ = li ± ri θi ± L ± ri θ n n with l i - nominal extension at θ = 0 an r i j is the raius of the pulley at the j th joint. he sign epens on whether the tenon path gets longer or shorter when the angle is change in a positive sense. he tenon connection, propose is a classical one, as is exemplifie in the Figure 5.

4 he pulling on the tenons route to the outer joints (tenons an 4 generates torques on the first joint as well as the secon joint. Figure 5. Geometrical escription of tenon riven finger he extension function of the form is: a θ h ( θ = l + a + b cos tan + b ( b θ > 0, while the bottom tenon satisfies: ( θ l Rθ h = + θ > 0, when θ < 0 these relations are reverse. Once the tenon extension functions have been compute, we can etermine the relationships between the tenon forces an the joint torques by p applying conservation of energy. Let e = h( θ R represent the vector of tenon extensions for a system with p tenons an efine the matrix nxp h P( θ R as P ( θ = ( θ. h hen ( θ & e & = θ = P ( θ θ &. Since the work one by the tenons must equal that one by the fingers, we can use conservation of energy to conclue p τ = P( θ f where f R is the vector of forces applie to the ens of the tenons. he matrix P ( θ is calle the coupling matrix. he extension functions for the tenon network are calculate by aing the contribution from each joint. he two tenons attache to the first joint are route across a pulley of raius R, an hence h = l Rθ (4 h = l + Rθ (5 he tenons for the outer link have more complicate kinematics ue to the routing through the tenon sheaths. heir extension functions are a θ h = l + a + b cos tan + b Rθ b (6 h 4 = l4 + Rθ + Rθ (7 he coupling matrix for the finger is compute irectly from extension functions: P ( θ h a = = + b sin tan 0 a + b θ R 0 R R R R (8 4 NUMERICAL SIMULAIONS Base on the theoretical backgroun presente, numerical simulations are require in orer to evaluate the efficiency of real mechanism. For flexible stuies all the elements are evelope as configurable Simulink blocks: - Shape memory alloy wire block presente in the section of article - Dynamics of two link fingers block base on equation from section - Coupling block base on equations evelope in section. Connecting all this blocks, for numerical simulations the following parameters are use: for the elements of the finger: - with = cm - length = 0 cm - mass = 5 g - raius pulley = cm - height = cm shape memory alloy parameters: - start temperature of martensitic state = 60 0 C - final temperature of martensitic state = 0 0 C - start temperature of austenite state = 50 0 C - final temperature of austenite state = 00 0 C - lower force evelope by the SMA M =.5 N - higher force evelope by the SMA M = 5 N

5 Figure 6. System moel he results of numerical simulations are: For the element of the finger: 5 CONCLUSIONS he simulations an the mathematical moel evelope in the article offer a backgroun in stuying the finger control possibilities. he results respect the real evolution of the structure. Notice that the influence of the evolution, in the evolution of the angle is strong. he simulations using higher frequency for the energizing the shape memory alloy conuct to a stable state, because of the material hysterezis an the thermal elay. All this elements conuct to a favourable conclusion concerning the mathematical moel valiity. In the future, the authors will explore all the control possibilities applie to a real moel, witch for the moment is uner construction. Figure 7. Force an angle evolution for element For the secon element of the finger: Figure 8. Force an angle evolution for element In the upper part of the figure is moelle the evolution of the SMA wire an in the lower part of the figure is the evolution of the angle θ i of the joint. In the mathematical moel the architectural limitation are implemente by imposing the angle π π evolution as θ i,. References: [] Bîzoacă N, Diaconu I., Hierarchical Control of a Smart Material Hyperreunant Cooperative Robots, ISR 00, Seoul, South Korea, 00. [] Bîzoacă N, Diaconu I., Shape memory alloy hyper-reunant robotic structure, CMM 00, Gliwice, Polan, 00. [] Delay L, Chanrasekaran M., Les Eitions Physique, Les Ulis, 987 [4] Graesser E.J., Cozarelli F.A., Journal of Intelligent Material Systems an Structures, 994 [5] Ivănescu M, Bîzoacă N., An Intelligent Control System for Hyperreunant Cooperative Robots, ISRA 000, Monterrey, Mexic, 000 [6] Ivănescu M., A New Manipulator Arms - A entacle Moel, Recent rens in Robotics, 984 [7] Schroeer B., Boller Ch., Comparative Assessment of Moels for Describing the Constitutive Behaviour of Shape Memory Alloy, Smart Materials an Structures, 998 [8] Stalmans R., Doctorate hesis, Catholic Univ. of Leuven, Dep. Of Metallurgy an Materials Science, 99 [9] Waram., Actuator Design Using Shape Memory Alloys,99 [0] Murray R.,Li Z., Sastry S., A mathematical introuction to robotic manipulation, CRC Press, 99